加速破壞性衰變模型之最佳實驗配置

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姓名	藍啟豪(Chi-Hao Lan) 查詢紙本館藏	畢業系所	統計研究所
論文名稱	加速破壞性衰變模型之最佳實驗配置 (Optimal Test Plans of Accelerated Destructive Degradation Models)
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摘要(中)	加速破壞性衰變試驗常用來評估一次性產品之可靠度資訊。而規劃此類型的計畫中，模型的假設、量測時間的選擇、應力水準的設定及其樣本配置的比例，皆會影響產品可靠度推論的精確性。本文將常用的加速破壞性衰變模型，加入具描述時間相關性之隨機過程，來配適實際資料以增加模型解釋之能力。利用類蒙地卡羅 (qusai-Monte Carlo) 方法來估計未知參數，且提供簡易流程來驗證衰變模型之適合性。最後，在模型參數是可辨別的條件下，提出最少試驗組合之D-最佳化實驗計畫。
摘要(英)	Accelerated destructive degradation tests (ADDTs) are commonly used to assess the reliability information of one-shot products. The accuracy of the reliability inference can be affected by the settings of test plan, including model assumptions, measurement times, stress levels and sample size allocations. This thesis takes stochastic processes into consideration in the traditional ADDT model to improve the ability of model interpretation. The qusai-Monte Carlo method is used to estimate the unknown parameters and a simple model-checking procedure is provided to assess the validity of different model assumptions. Finally, the D-optimal test plan with minimum run-size is proposed under the model assumption with identifiability.
關鍵字(中)	★ 加速破壞性衰變試驗 ★ 隨機過程 ★ 類蒙地卡羅 ★ 可辨別性 ★ D-最佳化	關鍵字(英)	★ accelerated destructive degradation tests ★ stochastic process ★ identifiability ★ qusai-Monte Carlo ★ D-optimality
論文目次	摘要 i Abstract ii 誌謝 iii 目錄 v 圖目錄 vii 表目錄 ix 第一章緒論 1 1.1 研究動機 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 文獻探討 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.3 研究方法 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.4 本文架構 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 第二章加速破壞性衰變模型之建立 5 2.1 加速破壞性衰變模型之一般式 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.1.1 具非單調隨機過程之加速破壞性模型 . . . . . . . . . . . . . . . . . . . . . 6 2.1.2具單調隨機過程之加速破壞性模型. . . . . . . . . . . . . . . . . . . . . . . . 8 2.2具批次效應和隨機過程之加速破壞性模型. . . . . . . . . . . . . . . . . . . . . 11 2.3 最大概似法 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.3.1 具維納過程之加速破壞性衰變模型參數估計. . . . . . . . . . . . . . . . . . . . 13 2.3.2具單調隨機過程之加速破壞性衰變模型參數估計. . . . . . . . . . . . . . . 15 2.4實例分析之模型選擇. . . . . . . . . . 23 2.4.1 濃硫酸容器資料. . . . . . . . . . . . . . . . . . . . . . 23 2.4.2 黏著劑B資料. . . . . . . . . . . . . . . . . . . . . . 26 2.4.3 黏著劑Ｋ資料. . . . . . . . . . . . . . . . . . . . . . 30 2.4.4 聚合物拉力比例資料. . . . . . . . . . . . . . . . . . 32 2.4.5 產品密封強度. . . . . . . . . . . . . . . . . . . . . . 34 第三章加速破壞性衰變模型之適合度檢定 39 3.1 產品壽命分配 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 3.1.1具維納過程之加速破壞性衰變模型的產品壽命分配. . . . . . . . . . . . . . . 39 3.1.2 具單調隨機過程之加速破壞性衰變模型的產品壽命分配. . . . . . . . . . . . . 42 3.2 虛擬失效時間. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 3.2.1 具截距隨機效應模型虛擬失效時間之估計. . . . . . . . . . . . . 44 3.2.2具斜率隨機效應模型虛擬失效時間之估計. . . . . . . . . . . . . 46 3.3 衰變模型之適合度檢定 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 3.4 實例分析之適合度檢定. . . . . . . . . . . . . . . . . 47 3.4.1 濃硫酸容器資料之適合度檢定. . . . . . . . . . . . . . . . . . . . . . 47 3.4.2 黏著劑B資料之適合度檢定. . . . . . . . . . . . . . . . . . . . . . 49 3.4.3 黏著劑Ｋ資料之適合度檢定. . . . . . . . . . . . . . . . . . . . . . 50 3.4.4 聚合物拉力比例資料之適合度檢定. . . . . . . . . . . . . . . . . . . . . . 51 3.4.5 產品密封強度之適合度檢定. . . . . . . . . . . . . . . . . . . . . . 52 第四章 D-最佳化實驗計畫 55 4.1 濃硫酸容器資料之D-最佳化實驗計畫. . . . . . . . . . . . . . . . . . . . . . 55 4.2 黏著劑B資料之D-最佳化實驗計畫. . . . . . . . . . . . . . . . . . . . . . 57 4.3 黏著劑Ｋ資料之D-最佳化實驗計畫. . . . . . . . . . . . . . . . . . . . . . 59 4.4 聚合物拉力比例資料之D-最佳化實驗計畫. . . . . . . . . . . . . . . . . 61 4.5 產品密封強度之D-最佳化實驗計畫. . . . . . . . . . . . . . . . . . . . . . 66 第五章結論與未來展望 71 附錄 72 參考文獻 94
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指導教授	樊采虹彭健育	審核日期	2018-12-13
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